Formation and switching of chiral magnetic field textures in three-dimensional gyroid nanostructures

Patterning of three-dimensional chiral nanostructures is an emerging route to engineering complex magnetization textures in magnetic systems, leading to a host of new physics and functionalities. However, a deep understanding of geometry-induced effects in magnetic nanostructures remains elusive due to complex nonlinear interplay among the long-range magnetic interactions, confined geometries, mechanical and magnetostatic multi-fields. Using finite-element-based micromagnetic simulations, we systematically investigate the magnetization textures and their responses under magnetic fields in Ni ₇₉Fe ₂₁ gyroid nanostructures with a wide range of solid volume fractions. Unusual magnetic field textures with the coexistence of left- and right-hand helices are formed in gyroid nanostructures in the absence of an external field. The ice rule governs the magnetic field textures in the gyroids with small solid volume fractions owing to the Y-shaped interconnections. However, a frustration of magnetic textures is observed in the gyroids with large solid volume fractions, which originates from the ice-rule breakdown due to the formation of antivortices. A critical value of volume fraction for the ice-rule breaking is determined at 30%. In addition, the switching of magnetic helical textures is demonstrated to be non-linearly dependent on the solid volume fraction of the gyroid nanostructures.